组卷网>知识点选题>对称性与奇偶性综合问题
显示知识点
显示答案
| 共计 232 道试题
单选题 | 一般(0.65) | 2021·肇州县第二中学
1 . 已知函数eqIdd489036e42c140acbd5be0414a28023a,且eqId97e0bb1d0e0f40f884e25f90ab6598aaeqId7dcd2312d0bf4bb1befdfcc170e45791上的奇函数,eqId7d6bb075fc7549f3a5f4eeecb5c27b54,则eqIda0b438c4ec864d9a93fdfd39c12f1925等于(   )
A.eqIdbeffaaf8d5cd43cf8375210d69fce6beB.eqId1d18010fc29e4f45abaaece953793246C.eqId8898c1dc81824f3098bbeae74e8f11fdD.eqIdddd35c5d043e4ebeac32a99367053c68
2 . 已知eqId10852d81bc184140a7780250c82c6929R上的奇函数.
(1)若当eqIdaa1312dcc8e24925b421f7767761a363时,eqIde3cb1fb2e6ce4099b8ea527544e1e419,求当eqId4db620a5946b4ee0a9f530f35a6d505aeqId10852d81bc184140a7780250c82c6929的解析式;
(2)若eqId10852d81bc184140a7780250c82c6929的最大值为M,求eqId10852d81bc184140a7780250c82c6929的最小值;
(3)若eqId5ffc7c2f9815413e9840f30c46b2cd77的最大值为M,最小值为m,则eqId001bdba8964b4f95a93ceda30fc7dbd3的值是多少?(只写结果)
3 . 有同学看到式子“eqId109a1015837e4340afa19d044e560d04”,理解为eqId208d361563fc48a699d9d584464c1a00是偶函数,且根据eqIdf82be817419a43debbf9bcee9feccc71eqId144eff5c0e4649138a21f2b1b6a06907的图像间的关系知eqId144eff5c0e4649138a21f2b1b6a06907的图像关于eqIdd5a6569623204652aada8c497a766e0a对称;请类比该同学的思路写出一个式子表示__________,eqId144eff5c0e4649138a21f2b1b6a06907的图像关于eqIdafed4da885124e6a9b4b7e8d5053b1e3对称.
解答题 | 一般(0.65) | 2020·慈溪中学高一月考
典型
4 . 已知函数eqIdecd9c8639ef741fca0c06b4adadf1abb
(1)当eqId5df9e339f957432c9aa2af743a279e68时,判断函数eqId10852d81bc184140a7780250c82c6929的奇偶性并证明;求出eqId10852d81bc184140a7780250c82c6929值域;
(2)给定实数eqId982da3835b7946d999cc8604a2ece266eqIdd951487aa2c84adebbd85d63425e0e52,问是否存在直线eqId02b4fd87b6dc469297673255c63eed1c,使得函数eqId10852d81bc184140a7780250c82c6929的图象关于直线eqId02b4fd87b6dc469297673255c63eed1c对称?若存在,求出eqId761b2917a82b4524b8dbab7e6380f014的值(用eqId70a27b6ddf6b478285353abb3b1f3741表示),若不存在,请说明理由.
单选题 | 一般(0.65) | 2021·江西(理)
5 . 已知函数fx)满足对任意实数mn,恒有eqIdfcb5cb88568f40808d2fc68326cfbcfdeqIdfa9e92bbc890417b816365cea798f88b,则eqIda874f394233a4d29ae0bd76e96b90667(   )
A.8080B.8082C.4040D.4041
6 . 已知函数eqId4d3e93a6d87549de932f2ff7ade9eadbeqId6fc94f6e181444c6b809fb393eb8fae6,有下列eqIdddd35c5d043e4ebeac32a99367053c68个命题:
①若eqIdf8f36afe46204fd483793db7e15fc0be为偶函数,则eqIde4a0e3706b56447b90fe1b2781f91b14的图象自身关于直线eqIdd5a6569623204652aada8c497a766e0a对称;
②函数eqIddbfb56004a1a409589aad7b03514d03feqId6db1730e304242ec8285c936cb021f08的图象关于直线eqIdd5a6569623204652aada8c497a766e0a对称:
③若eqIde4a0e3706b56447b90fe1b2781f91b14为奇函数,且eqId8c3df451b13d49c09202e64e9a197e43,则eqIde4a0e3706b56447b90fe1b2781f91b14的图象自身关于直线eqIdd5a6569623204652aada8c497a766e0a对称;
④若eqIde4a0e3706b56447b90fe1b2781f91b14为奇函数,且eqId0d936c9d474c4822a7d933ed91530d26,则eqIde4a0e3706b56447b90fe1b2781f91b14的图象自身关于直线eqIdd5a6569623204652aada8c497a766e0a对称;
其中正确命题的序号为______.
填空题 | 一般(0.65) | 2022·全国高三专题练习
7 . 已知函数eqId10852d81bc184140a7780250c82c6929是定义在eqId7dcd2312d0bf4bb1befdfcc170e45791上的奇函数,且当eqId26126945e23544d9b0cecaf9cf4809ac时,eqId94a10ad38ac9463d8994ea6228f5b189,则函数eqId86a526fef12641faa2f69857d7e72775的所有零点的和为_________
更新:2021/09/04组卷:189
8 . 已知函数eqIde55c05ba7c614501ab39af37b7e4dea8满足eqId5b9c582a93ae428cb261c3b67faa5c77,若函数eqId54d5de4a6cd74acfaa5e7f9cfb88086aeqIdd141790ec68b49e6b234c9105aa60c4b图像的交点为eqId9701f05e6cfe436093b29904d90381cf,则eqId4c7c18bedc414979bad19e37bc17b3e8____________.
单选题 | 较易(0.85) | 2021·江西(理)
9 . 已知函数eqId0d3af78a813c49bc81f08fc152c3a3d0的图像关于直线eqIdd5a6569623204652aada8c497a766e0a对称,且在eqIdde46290baec04ea1a59331d8d94f28df上单调递减,若eqId8b303f8e5acd48f9b7bc4ee85242b523eqId6c2baf445ee348d7b188a72822ec346eeqId9bcc5facf8ea4a4aa16e8c9d15b09d59,则eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqId44925af6fb19413689ba5616e3647cba的大小关系为(   )
A.eqId18513915a070416db1e6b2d279419695B.eqIdd267db4f512541f8825f9d0ff4192c96
C.eqId0b6548a2f82b4900bf8b5c24afd5ed7aD.eqId21670918e051478bbbcf459616d534f8
单选题 | 一般(0.65) | 2021·上海
10 . 函数eqId4ea41bfe1af14160957aa21d2d1d2434,其图象的对称轴是(   )
A.eqId90f4010cc71b4998be6fa90952078f6bB.eqIdd5a6569623204652aada8c497a766e0aC.eqId304afd9f2ec84e138ab539275a5edd19D.eqIdc5faa3a08c944a41850c52572707bcad
更新:2021/09/03组卷:110